The study of dynamical stability in planetary systems has become possible during the last few decades due to the development of numerical methods for long-term integrations of N-body systems. Since the 90’s the number of exoplanet detections has been increased significantly, making the simulations of other real planetary systems besides the Solar System feasible. One of the exciting new-found worlds is the system Kepler-11. Six planets which are located very close to each other orbit a solar-type star. In this project we first investigate the behavior of Kepler-11 when we change some of the initial conditions of the outermost planet of the system and then we approximate the Red Giant phase of solar-type stars in order to see how the planetary orbits are altered. For the first part we run three series of simulations (groups A,B,C). Each group has a different value for the mean density of planet Kepler-11g (1.0,1.5,2.0 g/cm 3 ). We run simulations for 36 different combinations of mass and eccentricity of planet Kepler-11g for each group. In nine configurations all six planets of the system continue to orbit the star until the end of the simulations. These nine stable configurations of Kepler-11 are used in the second part where we implement a constant mass-loss rate for the star which results in 30% mass loss after 30 million years, trying to approximate that way the mass loss of solar-type stars in Red Giant Branch. We also run nine simulations of a hypothetical system consisting only of the Sun, Earth and Jupiter where we implement the constant mass-loss rate to the Sun. In the Kepler-11 system, the orbits of planets Kepler-11g and Kepler-11e change by ∼45% and ∼54% respectively, after 30 million years, due to the mass loss of the star, while in the hypothetical planetary system the orbits of the two planets change by ∼43%. The study of orbits and how they move outward during the Post-Main Sequence evolution of stars is essential for our understanding of the existence of a Habitable Zone, not just around stars in Main-Sequence phase, but also around stars in late stages of their evolution.

In this paper, we write a summary about general relativity and, in particular,gravitational waves. We start by discussing the mathematics that generalrelativity uses, as well as the geometry in general relativity's spacetime. Afterwards,we explain linearized general relativity and derive the linearizedversions of Einstein's equations. From here, we construct wave solutionsand explain the polarization of gravitational waves. The quadrupole formulais derived, and generation and detection of gravitational waves is brie ydiscussed. Finally, LIGO and its latest discovery of gravitational waves isreviewed.

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Studying weak gravitational lensing of type Ia supernovae is a valuable tool to have in cosmology. Gravitational lensing may amplify the brightness of the source, affecting the brightness distribution of observed supernovae in a non-Gaussian way. Testing this magnified distribution for normality may thus reveal the observation of weak lensing. Simulation of lensing and studying the feasibility of current telescopes (ZTF) detecting it gives a first look into when this mechanism may be fully utilized.

In this research, the validity of using an effective potential to approximate general relativistic effects in an otherwise Newtonian setting was investigated, by making simulations of core collapse supernovae on one hand in full general relativity, and on the other hand in said Newtonian setting. This was done for a mass range covering progenitors of 12 − 60 solar masses; a much wider mass range than has been used in earlier research, that also includes progenitors that form black holes. Two numerical codes were used; the general relativistic hydrodynamic code GR1D, and the Newtonian hydrodynamic code FLASH. For simplicity, spherical symmetry was assumed, and a M1 neutrino transport was employed rather than solving the full Boltzmann transport equation for neutrinos. Three different versions of the effective potential; GREP1, GREP2, and GREP3, were tested, and their results compared to a general relativistic case; GR, in an attempt to investigate possible improvements of earlier research. For all parameters investigated in this research, case GREP1 (and GREP2) yielded results that agreed very well with case GR at the time around bounce, though somewhat worse later on in the evolution. This observation is consistent with that made by Marek et al. (2006), but for a much larger set of progenitors, and therefore, the reliability of using this version of the effective potential to approximate general relativistic effects in an otherwise Newtonian setting, is not only confirmed, but extended as well. Another exceptional result not seen before was the black 1 hole formation times, which all three effective potentials could reproduce within ∼ 5% compared to case GR. In addition to this, case GREP3 yielded excellent results for the central density, but rather poor results for the remaining properties, and is thus not recommended to use to approximate general relativistic effects, although further investigation of this potential might give valuable clues for further improvements

A non-zero helicity of cosmological magnetic fields could, if detected, have important implications for models of the electroweak phase transition in the early Universe. It has been suggested that the helicity of such a field could be related to the handedness of photon arrival directions in the diffuse gamma-ray sky observed by the \emph{Fermi} Large Area Telescope (LAT). \cite{tashiro_search_2014} found a left-handedness when applying this method, implying the existence of an extragalactic magnetic field with negative helicity. In this work the same method is applied, using twice as much data from the LAT due to the longer exposure time, providing higher statistical certainty. Additionally, the potential effects of the non-uniform LAT exposure and contamination of galactic emission are studied using simulated data sets. The results obtained indicate no significant signal, as the simulations suggest that the uncertainty was highly underestimated in \cite{tashiro_search_2014}, and any observed handedness using the updated LAT data is found to be compatible with zero within this new error estimate.

We propose a new method for detecting exoplanets using gravita-tional lensing. The hypothesis is that the lensing caused by an exo-planet could distort the structures of a radio background, for instancea H II region. It cannot be done with todays telescope but with thesecond incarnation of the Square Kilometer Array (SKA), currently inits design phase we deem it possible. In order to test this hypothesis weconstructed a simulation that creates a simple background structurewith variable scale and then produces simulated images such as theones achievable with the SKA. We produce positive result with a clearsignature of the planet with certain background scales and suggestfurther investigation into this method of detecting exoplanets.

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